Question:
In amplitude modulation, if the modulation index is \(0.8\) and the peak voltage of the message signal is \(10\,\text{V}\), then the amplitudes of the upper and lower side bands of the modulated wave are respectively
In amplitude modulation, if the modulation index is \(0.8\) and the peak voltage of the message signal is \(10\,\text{V}\), then the amplitudes of the upper and lower side bands of the modulated wave are respectively
Show Hint
For amplitude modulation,
\[
m=\frac{V_m}{V_c}
\]
and the amplitude of each sideband is
\[
V_{SB}=\frac{mV_c}{2}.
\]
The upper and lower sidebands always have equal amplitudes.
Updated On: Jul 9, 2026
- \(22.5\,\text{V},\;2.5\,\text{V}\)
- \(12.5\,\text{V},\;10\,\text{V}\)
- \(5\,\text{V},\;5\,\text{V}\)
- \(10\,\text{V},\;5\,\text{V}\) \bigskip
Show Solution
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The Correct Option is C
Solution and Explanation
Concept:
For an AM wave,
\[
m=\frac{V_m}{V_c},
\]
where
\[
m=\text{modulation index},
\quad
V_m=\text{peak message voltage},
\quad
V_c=\text{carrier peak voltage}.
\]
The amplitude of each sideband is
\[
V_{SB}=\frac{mV_c}{2}.
\]
The upper and lower sidebands have equal amplitudes.
Step 1: Calculate the carrier amplitude. Given, \[ m=0.8, \qquad V_m=10\,\text{V}. \] Using \[ m=\frac{V_m}{V_c}, \] \[ 0.8=\frac{10}{V_c}. \] \[ V_c=\frac{10}{0.8}. \] \[ V_c=12.5\,\text{V}. \]
Step 2: Find the amplitude of each sideband. \[ V_{SB} = \frac{mV_c}{2}. \] \[ V_{SB} = \frac{0.8\times12.5}{2}. \] \[ V_{SB} = \frac{10}{2}. \] \[ V_{SB}=5\,\text{V}. \]
Step 3: Write the amplitudes of USB and LSB. \[ V_{USB}=5\,\text{V}, \] \[ V_{LSB}=5\,\text{V}. \]
Step 4: Write the final answer. \[ \boxed{V_{USB}=5\,\text{V},\quad V_{LSB}=5\,\text{V}} \] \[ \boxed{\text{Answer = (C)}} \]
Step 1: Calculate the carrier amplitude. Given, \[ m=0.8, \qquad V_m=10\,\text{V}. \] Using \[ m=\frac{V_m}{V_c}, \] \[ 0.8=\frac{10}{V_c}. \] \[ V_c=\frac{10}{0.8}. \] \[ V_c=12.5\,\text{V}. \]
Step 2: Find the amplitude of each sideband. \[ V_{SB} = \frac{mV_c}{2}. \] \[ V_{SB} = \frac{0.8\times12.5}{2}. \] \[ V_{SB} = \frac{10}{2}. \] \[ V_{SB}=5\,\text{V}. \]
Step 3: Write the amplitudes of USB and LSB. \[ V_{USB}=5\,\text{V}, \] \[ V_{LSB}=5\,\text{V}. \]
Step 4: Write the final answer. \[ \boxed{V_{USB}=5\,\text{V},\quad V_{LSB}=5\,\text{V}} \] \[ \boxed{\text{Answer = (C)}} \]
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